Simplify square root of 9x^2* square root of 9y^5

$\sqrt{9 x^{2}} \cdot \sqrt{9 y^{5}}$

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$\sqrt{{(3 x)}^{2}} \cdot \sqrt{9 y^{5}}$

Pull terms out from under the radical, assuming positive real numbers.

$3 x \cdot \sqrt{9 y^{5}}$

Rewrite $9 y^{5}$ as ${(3 y^{2})}^{2} y$ .

Rewrite $9$ as $3^{2}$ .

$3 x \cdot \sqrt{3^{2} y^{5}}$

Factor out $y^{4}$ .

$3 x \cdot \sqrt{3^{2} (y^{4} y)}$

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$3 x \cdot \sqrt{3^{2} ({(y^{2})}^{2} y)}$

Rewrite $3^{2} {(y^{2})}^{2}$ as ${(3 y^{2})}^{2}$ .

$3 x \cdot \sqrt{{(3 y^{2})}^{2} y}$

Pull terms out from under the radical.

$3 x \cdot (3 y^{2} \sqrt{y})$

Multiply $3$ by $3$ .

$9 x y^{2} \sqrt{y}$